Solve for $x$ and $y$ using elimination. ${4x+3y = 43}$ ${3x+6y = 36}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-2$ ${-8x-6y = -86}$ $3x+6y = 36$ Add the top and bottom equations together. $-5x = -50$ $\dfrac{-5x}{{-5}} = \dfrac{-50}{{-5}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {4x+3y = 43}\thinspace$ to find $y$ ${4}{(10)}{ + 3y = 43}$ $40+3y = 43$ $40{-40} + 3y = 43{-40}$ $3y = 3$ $\dfrac{3y}{{3}} = \dfrac{3}{{3}}$ ${y = 1}$ You can also plug ${x = 10}$ into $\thinspace {3x+6y = 36}\thinspace$ and get the same answer for $y$ : ${3}{(10)}{ + 6y = 36}$ ${y = 1}$